In modern elevator systems having plural elevators, the elevator traffic is managed by a group control, which controls a plurality of elevators. The group control responds to calls from the passengers and determines with an allocation process which elevator is in each case optimal to be sent to serve the passenger. The call may be for instance a conventional up or down-type call, which includes the information of the direction where the passenger intends to travel. In the more moderns systems the call may be a destination call, which includes the destination information of the passenger. In the latter case, the group control implements so-called destination control system, in which each elevator user gives his/her personal destination information to the elevator system in the elevator lobby before boarding the elevator car. This is typically implemented with a destination call panel placed in the lobby of the elevator system. In a system using destination control, the destination information is the only necessary input from the passenger. After receiving the call including the destination information, i.e. the destination call, the system allocates an elevator for the passenger based on certain logic. After allocation, the elevator system schedules the allocated elevator to stop at the lobby of the passenger. At a suitable moment after the allocation, the system gives the passenger a signal identifying which one of the elevators has been allocated to him. Thereby, the passenger can start proceeding towards the door of the elevator in question. In prior art the signaling moment is usually immediately after the allocation. The immediate signaling is used in cases where the allocation process is started and finalized immediately after the call. This type of allocation process is known as immediate landing call allocation (ILA). The drawback of ILA is that any changes in call situation occurring after the end of the allocation process cannot be taken into account any more. In prior art, also such a solution is known where the signaling is not performed immediately after the allocation. In this solution the result of the allocation is not finalized nor signaled to the passenger until at the latest possible moment before the arrival of the car of the allocated elevator at the lobby where the passenger is. In this way the allocation process can be continued longer. This makes it possible that the allocation can be repeated after the initial allocation, and should the call situation change, the allocation can be changed too. Thereby, the system can take into account late changes in the call situation and optimize the operation of the elevators accordingly. The drawback of this system is that the passenger has to walk to the door of the elevator allocated for him/her in haste. In prior art, if such problems has been noticed in a certain elevator system, the system is reprogrammed such that the signaling takes place always before a fixed period of time before the arrival of the allocated car to the lobby.